Markus Hähkiöniemi

• PhD
• Senior Lecturer at University of Jyväskylä

This paper is a report of a study on how a less successful student perceives the derivative from the graph of a function. A task-based interview of a grade 11 student was analyzed to find how she perceived the derivative from a graph of a function and what kind of representations she used for this. The results show how she used representations of t...

Research on balance rule learning has focused on studies done in individual settings. This study investigates how students collaboratively learn balance rules and focuses especially on four variables that potentially affect rule development: student age, group composition, prior knowledge, and scientific reasoning skills. Eight-, ten- and twelve-ye...

Exercising agency is an inherent component of peer assessment. However, the research on agency in peer assessment is scarce. This case study explored how seventh grade science students exercised agency during formative peer assessment. The data comprises audio recordings of students’ classroom discussions, written peer feedback, written work, stude...

The purpose of this study is to investigate how teachers use different types of discourse to support dialogic argumentation. Dialogic argumentation is a collaborative process in which students construct arguments together and examine arguments presented by their peers. Science teachers can use argumentation as a vehicle to help students gain a work...

Previous studies have highlighted the importance of primary school students’ adaptive number knowledge, which includes knowledge of numerical characteristics and relations. In this study, students from the second (aged 8), fourth (aged 10), and sixth (aged 12) grades (n = 205) answered a modified version of the Arithmetic production task, which has...

In this study, educational dialogue is explored through informal formative assessment and dialogicity. We enhance the understanding of informal formative assessment and dialogicity by considering their relationship. Even though the interconnection of informal formative assessment and dialogicity is acknowledged, it has not been explicitly examined...

Previous studies have proposed that students’ mathematical understanding develops dynamically through the process known as folding back, in which learners revisit earlier forms of understanding and use them to build even deeper levels of mathematical understanding. Digital learning environments, where students can manipulate representations, are of...

Teacher telling can support but also hinder learning. In inquiry activities, telling that removes productive struggle may be problematic. In this study, different aged students experimented in a digital learning environment to build rules for a balance beam. We examined how the amount of teacher telling vary according to students' age and the sophi...

There is a need for research on the effect of different types of model progressions and learner age on learning and engagement in inquiry-based science settings. This study builds on the Scientific Discovery as Dual Search model to introduce less specific implicit model progression and compares them to the traditional explicit model progression. Th...

In this study, we focus on dialogic argumentation among students in a whole class setting in mathematics and physics in lower secondary school. By drawing on previous studies on the structure of argumentation and dialogic interactions, we suggest that transparency of student reasoning and students' engagement with each other's ideas are two key asp...

In this chapter, I examine argumentation from the perspective of dialogic argumentation that highlights students’ engagement with each other’s ideas in the process of making mathematical claims and providing evidence to support them. I analyzed the provided data for students’ dialogic and justifying moves and investigated how the teacher supported...

Research related to dialogic teaching has been gaining ground in recent decades. On a theoretical level, researchers have described how sociocultural approaches are linked to dialogic teaching. In addition, empirical studies have explained how dialogic teaching manifests itself in educational dialogue and classroom interactions. However, studies ad...

Dynamic representations (e.g., dynamic geometry software GeoGebra for mathematics learning and PhET simulations for science learning) offer excellent opportunities for students to conduct investigations and to formulate explanations for the visualized phenomena. In order for this to be effective, students need guidance, for example, for planning th...

Tässä tutkimuksessa tarkastellaan, miten oppilaslähtöisyys ja dialogisuus ilmenevät matematiikassa ja miten ne kytkeytyvät toisiinsa erityisesti oppilaiden näkökulmien, ajatusten ja kokemusten huomioimisen kautta. Tutkimuksen aineistoksi valittiin matematiikan aineenopettajaopiskelijoiden pitämiä oppitunteja, joissa havaittiin keskimääräisesti enem...

A growing body of research has recognized the importance of students' having active roles in feedback processes. Feedback literacy refers to students' understandings of and participation in feedback processes, and research on students' feedback literacy has so far focused on higher education; secondary schools have not received attention. This case...

This case study examined teachers’ on-the-fly formative assessment conversations, that is, how teachers collect information from students’ thinking and use that information to support their learning during teacher-student interactions. Previous studies have typically analysed whole-class discussions on the level of speaking turns, and have identifi...

Peer assessment has been shown to advance learning, for example, by improving one’s work, but the variance of learning benefits within or between studies has not been explained. The purpose of this case study was to examine what kinds of pathways students have through peer assessment and to study which factors affect them when peer assessment is im...

Open access: https://doi.org/10.5817/SP2019-4-9 Abstract: Three dimensions of dialogicity are emphasised in the literature: dialogic teacher talk, students' dialogic moves and organising for dialogic teaching. In this article, we examine these dimensions and the interplay between them in supporting dialogic argumentation in the context of whole-cl...

When implementing a problem-solving lesson, the teacher needs to provide students appropriate guidance during problem solving. This demanding task requires understanding students’ work in progress and giving them necessary help without constraining their thinking. In this article, we share insights from two professional development programs on how...

Whereas science is fundamentally a result of a dialogic debate, the authoritative approach has been conceived of as a fundamental part of school science. Dialogic interactions encompass the mutual appreciation of different ideas manifested in teacher supportiveness toward students and, in authoritative interactions, the focus is more on the science...

In this study, we analyse how 7th grade students’ engagement during small group work differed in two consecutive algebra lessons: in the first lesson students solved equations and in the second lesson they created equations for other small groups to solve. Data was collected by videorecording the work of two groups in both lessons. Through directed...

Inquiry activities generate rich opportunities for STEM learning and for assessment. When teachers pay attention to assessment information collected during the course of learning, they are able to interpret and make decisions about such assessment data in a timely fashion that can drive future planning and support student learning, for example thro...

This paper reports on a teacher professional development (PD) programme addressing dialogic argumentation in mathematics and science classrooms. While argumentation skills are becoming more and more important in an increasingly polarised society, the social aspect of argumentation is often neglected in secondary education. Moreover, it is agreed th...

Previous studies have produced several typologies of teacher questions in mathematics. Probing questions that ask students to explain are often included in the types of questions. However, only rare studies have created subtypes for probing questions or investigated how questioning differs depending on whether technology is used or not. The aims of...

The interaction between the teacher and the learners when using simulations is in need of research. This study concentrates on two questioning approaches, series of probing and series of guiding questions that teachers use to guide learning with simulations. These two approaches are contrasted with non-directive and directive guidance provided by t...

This paper is focused on the characterization of informal formative assessment conversations (i.e., interactions on-the-fly) from a methodological perspective. Interactions on-the-fly are unexpected teachable moments in which the teacher tries to probe students' understanding and use that information to support their inquiry process. One of the cod...

The adoption of Inquiry Based Science Education (IBSE) has been a policy priority over the last decade in Europe. IBSE pedagogy cannot be dissociated from the assessment of inquiry skills. Assess Inquiry in Science, Technology and Mathematics Education (ASSIST-ME) is one of the two FP7 projects that are contributing to developing our understanding...

In schools, classroom talk is often dominated by teachers´ lecturing or asking closed questions followed by teachers’ evaluative feedback. When the teacher presents ideas to students or uses the question-response feedback, the talk is considered as authoritative talk. On the other side, during dialogic talk, the teacher reacts to students´ views an...

Getting students to explain their thinking is one of the big challenges in teachers' work. Previous studies have analysed teacher questioning by focusing on amounts of different types of questions. In this study, I use questioning diagrams to see how questioning develops during the lessons. The data includes video recordings of student teachers' ma...

According to previous studies, inquiry-based mathematics teaching enhances learning. However, teachers need support in implementing this type of teaching. In this study, a high school teacher was given a short preplanned inquiry-based mathematics teaching unit that included activities with GeoGebra. The teacher was interviewed after every lesson to...

Previous research has developed several problem-solving models and suggested that the teacher plays a crucial role in guiding students’ problem solving. However, less is known about the particularities of problem solving and teacher guidance when dealing with open problems which include multiple possible solution pathways. The aim of this study is...

Previous studies have proposed that students’ mathematical understanding develops dynamically through the process known as folding back, in which learners revisit earlier forms of understanding and use them to build even deeper levels of mathematical understanding. Digital learning environments, where students can manipulate representations, are of...

In this paper, we study how prospective teachers guide students' reasoning in GeoGebra-supported inquiry tasks. Twenty prospective mathematics teachers wrote about how they would react as a teacher in hypothetical situations where high school students present their GeoGebrasupported solutions to the teacher. Before writing their reactions, the pros...

There is a growing movement toward the introduction of algebra in early grades. This is supported by an increasing number of research studies that have reported success in getting young students to “do” mathematics considered beyond their reach. Yet, the consensus is that more research is needed to provide insights into the processes by which stude...

This paper reports how an advanced 11th-grade student (Daniel) perceived the derivative from a graph of a function at a task-based interview after a short introduction to the derivative. Daniel made very impressive observations using, for example, the steepness and the increase of a graph as well as the slope of a tangent as representations of the...

This paper reports a study of how students may connect the limiting process inherent in the derivative to the limit of the difference quotient (LDQ) when solving problems. The data was collected mainly through task-based interviews with five eleventh grade students. It was found that the students used various kinds of limiting processes and connect...

Tiivistelmä: Representaatioiden merkitys derivaatan oppimisessa. Diss. -- Jyväskylän yliopisto.

In this paper we study how a student begins to acquire the concept of the derivative, what kind of representations he acquires and how he connects these representations. A teaching period, in which different perceptual and symbolic representation were emphasized, was carried out and task based interviews conducted to five students. The students use...

In this paper I study meaningfulness and durability of five high-school students' knowledge of the derivative concept. The students had been taught the derivative emphasizing graphical properties of the derivative and limiting processes inherent in the derivative. They participated in two task-based interviews: one administered when they were study...

This research examines the mathematical activity of a group of eight-grade students who participated in open-ended mathematical investigations of quadratic functions. In particular, the study traces the students' mathematical reasoning and notation as they work on determining rules of quadratic functions. The study is also an outgrowth of a 3-Year...

Task based interviews to five postsecondary students were arranged to investigate the students' understanding of the limit of the difference quotient. The students' proce-dural understanding was analysed by using the APOS-theory and their conceptual understanding was analysed by examining what kind of representations they had of the limiting proces...